If 8 children ate a crate of egg in 12 days, how long will it take 6 children to eat same crate of egg at the same rate

It will take 16 days.

We first find the rate that each child eats eggs at.  30 eggs in 12 days = 30/12 = 5/2 for all 8 children.  Dividing this by 8 to find the rate per child,

5/2 ÷ 8/1 = 5/2 × 1/8 = 5/16

Multiply this rate per child by the number of children:  5/16(6) = 30/16

30 eggs would be eaten in 16 days.